Mechanics of encapsulated droplets

Abstract

A capsule consists of an internal medium (pure or complex liquid), enclosed by a deformable membrane that is usually semi-permeable. Capsules are frequently met in nature (living cells) or in industrial processes (pharmaceutical, cosmetic or food industry). The motion, deformation and burst of a capsule under stress depend on three types of independent intrinsic physical properties: initial geometry, internal liquid viscosity and interface constitutive behavior. The direct determination of the latter is difficult owing to the thinness and fragility of the interface. Over the years different techniques have been used (compression between two flat plates, micropipette aspiration, etc.). Recently, a new technique has been proposed, that consists in placing a capsule on the axis of a spinning drop tensiometer. The deformation under increasing rotation rates is measured, and a mechanical model allows to compute the elastic modulus of the membrane.

Another line of approach consists in suspending a capsule in another liquid subjected to flow and in measuring the resulting deformation. In order to relate the overall capsule deformation to the particle intrinsic physical parameters, a fairly complete model of the mechanics of the particle is necessary. Analytical models have been obtained for initially spherical capsules, subjected to small deformations (less than 10–15%), with simple membrane constitutive laws (rubber elasticity, viscoelasticity, area incompressibility). They allow to infer the membrane apparent elastic modulus from deformation vs. shear rate curves obtained for artificial capsules. For large deformations and non-spherical initial shapes, numerical models have been proposed. For example, break-up of a capsule under an elongational shear is predicted. It is also possible to model the flow of a large capsule through a small short pore or through a long cylindrical tube that has a smaller diameter than the capsule.